In our extension of the SM with a complex singlet scalar, the SM-like Higgs boson coupling strengths to other SM particles are modified by
a common factor of \(\cos \theta \) . This leads to the productions of \(X\bar{X}\)  (where \(X\)  can be a SM gauge boson or fermion) via the SM-like Higgs boson being suppressed by a factor \(\cos ^2\theta \) , provided that no additional decay channel is permitted. Note that the same factor of \(\cos ^2\theta \)  is involved in all major production channels (gluon fusion, vector boson fusion and \(t \overline{t} h\) ).
To take into account the published exclusion bounds from Higgs searches at the LEP, Tevatron and LHC experiments, we make use of the
\(\textsf {HiggsBounds}\_\textsf {v4.3.1}\)  [1]} package, which calculates the predicted signal rates for
the search channels considered in the experimental data.
More information on search channels and experimental data used in \(\textsf {HiggsBounds}\)  can be found in Ref. [1]}.
The \(\textsf {HiggsBounds}\)  package determines whether a point in the model parameter space is excluded at 95% CL by comparing the predicted signal rates against the expected and observed cross section limits from the
direct Higgs searches [1]}.
